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      SUBROUTINE <a name="DTRTRI.1"></a><a href="dtrtri.f.html#DTRTRI.1">DTRTRI</a>( UPLO, DIAG, N, A, LDA, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          DIAG, UPLO
      INTEGER            INFO, LDA, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   A( LDA, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DTRTRI.18"></a><a href="dtrtri.f.html#DTRTRI.1">DTRTRI</a> computes the inverse of a real upper or lower triangular
</span><span class="comment">*</span><span class="comment">  matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  This is the Level 3 BLAS version of the algorithm.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'U':  A is upper triangular;
</span><span class="comment">*</span><span class="comment">          = 'L':  A is lower triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DIAG    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  A is non-unit triangular;
</span><span class="comment">*</span><span class="comment">          = 'U':  A is unit triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the triangular matrix A.  If UPLO = 'U', the
</span><span class="comment">*</span><span class="comment">          leading N-by-N upper triangular part of the array A contains
</span><span class="comment">*</span><span class="comment">          the upper triangular matrix, and the strictly lower
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.  If UPLO = 'L', the
</span><span class="comment">*</span><span class="comment">          leading N-by-N lower triangular part of the array A contains
</span><span class="comment">*</span><span class="comment">          the lower triangular matrix, and the strictly upper
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.  If DIAG = 'U', the
</span><span class="comment">*</span><span class="comment">          diagonal elements of A are also not referenced and are
</span><span class="comment">*</span><span class="comment">          assumed to be 1.
</span><span class="comment">*</span><span class="comment">          On exit, the (triangular) inverse of the original matrix, in
</span><span class="comment">*</span><span class="comment">          the same storage format.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0: successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0: if INFO = i, A(i,i) is exactly zero.  The triangular
</span><span class="comment">*</span><span class="comment">               matrix is singular and its inverse can not be computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            NOUNIT, UPPER
      INTEGER            J, JB, NB, NN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.70"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.71"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>
      EXTERNAL           <a name="LSAME.72"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.72"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           DTRMM, DTRSM, <a name="DTRTI2.75"></a><a href="dtrti2.f.html#DTRTI2.1">DTRTI2</a>, <a name="XERBLA.75"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      UPPER = <a name="LSAME.85"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      NOUNIT = <a name="LSAME.86"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIAG, <span class="string">'N'</span> )
      IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.87"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) THEN
         INFO = -1
      ELSE IF( .NOT.NOUNIT .AND. .NOT.<a name="LSAME.89"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIAG, <span class="string">'U'</span> ) ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.97"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DTRTRI.97"></a><a href="dtrtri.f.html#DTRTRI.1">DTRTRI</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Check for singularity if non-unit.
</span><span class="comment">*</span><span class="comment">
</span>      IF( NOUNIT ) THEN
         DO 10 INFO = 1, N
            IF( A( INFO, INFO ).EQ.ZERO )
     $         RETURN
   10    CONTINUE
         INFO = 0
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Determine the block size for this environment.
</span><span class="comment">*</span><span class="comment">
</span>      NB = <a name="ILAENV.118"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 1, <span class="string">'<a name="DTRTRI.118"></a><a href="dtrtri.f.html#DTRTRI.1">DTRTRI</a>'</span>, UPLO // DIAG, N, -1, -1, -1 )
      IF( NB.LE.1 .OR. NB.GE.N ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Use unblocked code
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="DTRTI2.123"></a><a href="dtrti2.f.html#DTRTI2.1">DTRTI2</a>( UPLO, DIAG, N, A, LDA, INFO )
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Use blocked code
</span><span class="comment">*</span><span class="comment">
</span>         IF( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute inverse of upper triangular matrix
</span><span class="comment">*</span><span class="comment">
</span>            DO 20 J = 1, N, NB
               JB = MIN( NB, N-J+1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute rows 1:j-1 of current block column
</span><span class="comment">*</span><span class="comment">
</span>               CALL DTRMM( <span class="string">'Left'</span>, <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, DIAG, J-1,
     $                     JB, ONE, A, LDA, A( 1, J ), LDA )
               CALL DTRSM( <span class="string">'Right'</span>, <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, DIAG, J-1,
     $                     JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute inverse of current diagonal block
</span><span class="comment">*</span><span class="comment">
</span>               CALL <a name="DTRTI2.144"></a><a href="dtrti2.f.html#DTRTI2.1">DTRTI2</a>( <span class="string">'Upper'</span>, DIAG, JB, A( J, J ), LDA, INFO )
   20       CONTINUE
         ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute inverse of lower triangular matrix
</span><span class="comment">*</span><span class="comment">
</span>            NN = ( ( N-1 ) / NB )*NB + 1
            DO 30 J = NN, 1, -NB
               JB = MIN( NB, N-J+1 )
               IF( J+JB.LE.N ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Compute rows j+jb:n of current block column
</span><span class="comment">*</span><span class="comment">
</span>                  CALL DTRMM( <span class="string">'Left'</span>, <span class="string">'Lower'</span>, <span class="string">'No transpose'</span>, DIAG,
     $                        N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA,
     $                        A( J+JB, J ), LDA )
                  CALL DTRSM( <span class="string">'Right'</span>, <span class="string">'Lower'</span>, <span class="string">'No transpose'</span>, DIAG,
     $                        N-J-JB+1, JB, -ONE, A( J, J ), LDA,
     $                        A( J+JB, J ), LDA )
               END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute inverse of current diagonal block
</span><span class="comment">*</span><span class="comment">
</span>               CALL <a name="DTRTI2.167"></a><a href="dtrti2.f.html#DTRTI2.1">DTRTI2</a>( <span class="string">'Lower'</span>, DIAG, JB, A( J, J ), LDA, INFO )
   30       CONTINUE
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DTRTRI.174"></a><a href="dtrtri.f.html#DTRTRI.1">DTRTRI</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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